In a force balanced sensing instrument, such as an accelerometer for example, it is generally desired that the instrument output signal be proportional to the input condition to be sensed. Therefore, in many types of electrostatic and electromagnetic force balanced sensing instruments special techniques are required to obtain a linear relation between the instrument output and the sensed input. In electrostatic and electromagnetic instruments, the forces applied by the instrument forcer are not linearly related to the feedback voltage or current supplied to the forcer. Furthermore, for optimum operation of the instrument itself it is preferred that the feedback force applied by the feedback control network have a linear relation to the sensed input. Thus, special techniques have been employed for obtaining such linearity.
As one example, in an electrostatic force balanced accelerometer, electrostatic forcing in a closed loop system is employed to position and obtain an output from an inertial mass or proof mass. The electrostatic forcing system employs a capacitive pickoff electrode on each side of a pendulous member that has been etched from a silicon substrate. A control pulse is employed to sequentially apply a constant amount of charge to each electrode. A variable force is applied to the inertial mass by varying the amount of time (e.g., duty cycle) the charge is left on a respective plate. The amount of time the charge is left on a respective plate is based on the displacement of the inertial mass relative to a null position.
Therefore, the feedback system in a given accelerometer mechanization is designed to equalize the measured capacitance on both sides of the inertial mass to maintain the inertial mass at the null position. As a result, the proof mass is moved to the position required to equalize the measured capacitance, regardless of how much displacement this causes relative to the suspension. It is typically assumed that when the capacitances are equal on both sides of the inertial mass, the accelerometer forms a pair of parallel-plate capacitors. However, a number of mechanical and electrical factors can contribute to a non-uniform distribution of charge and/or an error in the magnitude of the effective applied charge on the pickoff electrodes on either side of the inertial mass, thus resulting in errors in the measurement of the specific force input to the inertial mass by an external influence, such as acceleration.